Abstract
A clique-transversal set S of a graph G is a subset of vertices intersecting all the cliques of G, where a clique is a complete subgraph maximal under inclusion and having at least two vertices. A clique-independent set of the graph G is a set of pairwise disjoint cliques of G. The clique-transversal number τ C ( G ) of G is the cardinality of the smallest clique-transversal set in G and the clique-independence number α C ( G ) of G is the cardinality of the largest clique-independent set in G. This paper proves that determining τ C ( G ) and α C ( G ) is NP-complete for a cubic planar graph G of girth 3. Further we propose two approximation algorithms for determining τ C ( G ) and α C ( G ) in a cubic graph G.
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